The Experts below are selected from a list of 360 Experts worldwide ranked by ideXlab platform
Jianhui Huang - One of the best experts on this subject based on the ideXlab platform.
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social optima in mean field Linear Quadratic Gaussian control with volatility uncertainty
Siam Journal on Control and Optimization, 2021Co-Authors: Jianhui Huang, Bingchang Wang, Jiongmin YongAbstract:This paper examines mean field Linear-Quadratic-Gaussian social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility p...
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Linear Quadratic Gaussian mean field game with partial observation and common noise
Mathematical Control and Related Fields, 2021Co-Authors: Alain Bensoussan, Xinwei Feng, Jianhui HuangAbstract:This paper considers a class of Linear-Quadratic-Gaussian (LQG) mean-field games (MFGs) with partial observation structure for individual agents. Unlike other literature, there are some special features in our formulation. First, the individual state is driven by some common-noise due to the external factor and the state-average thus becomes a random process instead of a deterministic quantity. Second, the sensor function of individual observation depends on state-average thus the agents are coupled in triple manner: not only in their states and cost functionals, but also through their observation mechanism. The decentralized strategies for individual agents are derived by the Kalman filtering and separation principle. The consistency condition is obtained which is equivalent to the wellposedness of some forward-backward stochastic differential equation (FBSDE) driven by common noise. Finally, the related \begin{document}$ \epsilon $\end{document} -Nash equilibrium property is verified.
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social optima in mean field Linear Quadratic Gaussian control with volatility uncertainty
arXiv: Optimization and Control, 2019Co-Authors: Jianhui Huang, Bingchang Wang, Jiongmin YongAbstract:This paper examines mean field Linear-Quadratic-Gaussian (LQG) social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility process driven by a common noise. We apply a robust optimization approach in which all agents view volatility uncertainty as an adversarial player. Based on the principle of person-by-person optimality and a two-step-duality technique for stochastic variational analysis, we construct an auxiliary optimal control problem for a representative agent. Through solving this problem combined with a consistent mean field approximation, we design a set of decentralized strategies, which are further shown to be asymptotically social optimal by perturbation analysis.
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Linear Quadratic Gaussian mixed mean field games with heterogeneous input constraints
Siam Journal on Control and Optimization, 2018Co-Authors: Jianhui Huang, Tianyang NieAbstract:We consider a class of Linear-Quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents with mean-field interactions. The individual admissible controls are constrained in closed convex subsets $Γ k$ of full space $R m$. The decentralized strategies for individual agents and consistency condition system are represented in an unified manner via a class of mean-field forward-backward stochastic differential equations involving projection operators on $Γ k$. The well-posedness of consistency system is established in the local and global cases both by the contraction mapping and discounting method respectively. The related $e$−Nash equilibrium property is also verified.
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Linear Quadratic Gaussian mixed mean field games with heterogeneous input constraints
arXiv: Optimization and Control, 2017Co-Authors: Jianhui Huang, Tianyang NieAbstract:We consider a class of Linear-Quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets $\Gamma_{k}$ of $\mathbb{R}^{m}.$ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on $\Gamma_{k}$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\varepsilon-$Nash equilibrium property is also verified.
Tianxiao Wang - One of the best experts on this subject based on the ideXlab platform.
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mean field Linear Quadratic Gaussian lqg games for stochastic integral systems
IEEE Transactions on Automatic Control, 2016Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this technical note, we formulate and investigate a class of mean-field Linear-Quadratic-Gaussian (LQG) games for stochastic integral systems. Unlike other literature on mean-field games where the individual states follow the controlled stochastic differential equations (SDEs), the individual states in our large-population system are characterized by a class of stochastic Volterra-type integral equations. We obtain the Nash certainty equivalence (NCE) equation and hence derive the set of associated decentralized strategies. The $\epsilon$ -Nash equilibrium properties are also verified. Due to the intrinsic integral structure, the techniques and estimates applied here are significantly different from those existing results in mean-field LQG games for stochastic differential systems. For example, some Fredholm equation in the mean-field setup is introduced for the first time. As for applications, two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system, and relevant mean-field LQG games are discussed.
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mean field Linear Quadratic Gaussian lqg games for stochastic integral systems
arXiv: Probability, 2013Co-Authors: Jianhui Huang, Tianxiao WangAbstract:In this paper we discuss a class of mean field Linear-Quadratic-Gaussian (LQG) games for large population system which has never been addressed by existing literature. The features of our works are sketched as follows. First of all, our state is modeled by stochastic Volterra-type equation which leads to some new study on stochastic "integral" system. This feature makes our setup significantly different from the previous mean field games where the states always follow some stochastic "differential" equations. Actually, our stochastic integral system is rather general and can be viewed as natural generalization of stochastic differential equations. In addition, it also includes some types of stochastic delayed systems as its special cases. Second, some new techniques are explored to tackle our mean-field LQG games due to the special structure of integral system. For example, unlike the Riccati equation in Linear controlled differential system, some Fredholm-type equations are introduced to characterize the consistency condition of our integral system via the resolvent kernels. Third, based on the state aggregation technique, the Nash certainty equivalence (NCE) equation is derived and the set of associated decentralized controls are verified to satisfy the $\epsilon$-Nash equilibrium property. To this end, some new estimates of stochastic Volterra equations are developed which also have their own interests.
H J Chizeck - One of the best experts on this subject based on the ideXlab platform.
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jump Linear Quadratic Gaussian control in continuous time
IEEE Transactions on Automatic Control, 1992Co-Authors: H J ChizeckAbstract:The optimal Quadratic control of continuous-time Linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes is addressed. The systems are also subject to Gaussian input and measurement noise. The optimal solution for the jump Linear-Quadratic-Gaussian (JLQC) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample-path dependent. If the plant parameters are constant in each value of the underlying jumping process, then the controller portion of the compensator converges to a time-invariant control law. However, the filter portion of the optimal infinite time horizon JLQC compensator is not time invariant. Thus, a suboptimal filter which does converge to a steady-state solution (under certain conditions) is derived, and a time-invariant compensator is obtained. >
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jump Linear Quadratic Gaussian control in continuous time
American Control Conference, 1991Co-Authors: H J ChizeckAbstract:This paper is concerned with the optimal Quadratic control of continuous-time Linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes. The systems are also subject to Gaussian input and measurement noises. This Jump Linear Quadratic Gaussian (JLQG) optimal control problem can be used to consider the control of systems which are subject to abrupt changes in their structure and components and also with disturbances on actuators and sensors. The solution of the continuous-time Jump Linear Quadratic (JLQ) problem, (the JLQG problem with complete state information and no input noise) is known. However in many applications, the plant state is available only through noisy observations on the output channel. In this paper, the optimal solution for the JLQG problem in finite time is given. This solution is based on a separation theorem. The optimal state estimator is sample path dependent (it may depend upon past as well as the current values of the jump parameter). For the infinite time JLQG problem, the optimal solution is also obtained. If the plant parameters are constant in each value of the underlying jumping process, then the controller part of the compensator converges to a time invariant control law (which depends on the jump parameter). However the filter portion of the optimal infinite time horizon JLQG compensator is not time invariant. A suboptimal filter which does converge to a steady-state solution (under certain stochastic stabilizabilty and observability conditions) is also derived.
Ali Shahdi - One of the best experts on this subject based on the ideXlab platform.
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discrete time Linear Quadratic Gaussian control for teleoperation under communication time delay
The International Journal of Robotics Research, 2006Co-Authors: Shahin Sirouspour, Ali ShahdiAbstract:Prior relevant research in bilateral teleoperation has mainly yielded control algorithms that sacrifice performance in order to guarantee robust stability in the presence of communication latency. In contrast, in this paper we propose a multimodel predictive-type control approach based on the discrete-time Linear Quadratic Gaussian (LQG) control that delivers a stable transparent response in the presence of constant delay. Separate controllers are designed for different phases of operation, i.e., free motion/soft contact and contact with rigid environments, with switching between these mode-based controllers occurring according to the identified contact mode. The treatment of the problem in the discrete-time domain allows for the development of a finite dimension state-space model that explicitly encompasses the time delay. Performance objectives such as position tracking and tool impedance shaping for free motion/soft contact, as well as position and force tracking for contact with rigid environments, ar...
Silvere Bonnabel - One of the best experts on this subject based on the ideXlab platform.
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an invariant Linear Quadratic Gaussian controller for a simplified car
International Conference on Robotics and Automation, 2015Co-Authors: Sebastien Diemer, Silvere BonnabelAbstract:In this paper, we consider the problem of tracking a reference trajectory for a simplified car model based on unicycle kinematics, whose position only is measured, and where the control input and the measurements are corrupted by independent Gaussian noises. To tackle this problem we devise a novel observer-controller: the invariant Linear Quadratic Gaussian controller (ILQG). It is based on the Linear Quadratic Gaussian controller, but the equations are slightly modified to account for, and to exploit, the symmetries of the problem. The gain tuning exhibits a reduced dependency on the estimated trajectory, and is thus less sensitive to misestimates. Beyond the fact the invariant approach is sensible (there is no reason why the controller performance should depend on whether the reference trajectory is heading west or south), we show through simulations that the ILQG outperforms the conventional LQG controller in case of large noises or large initial uncertainties.
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an invariant Linear Quadratic Gaussian controller for a simplified car
arXiv: Robotics, 2014Co-Authors: Sebastien Diemer, Silvere BonnabelAbstract:In this paper, we consider the problem of tracking a reference trajectory for a simplified car model based on unicycle kinematics, whose position only is measured, and where the control input and the measurements are corrupted by independent Gaussian noises. To tackle this problem we devise a novel observer-controller: the invariant Linear Quadratic Gaussian controller (ILQG). It is based on the Linear Quadratic Gaussian controller, but the equations are slightly modified to account for, and to exploit, the symmetries of the problem. The gain tuning exhibits a reduced dependency on the estimated trajectory, and is thus less sensitive to misestimates. Beyond the fact the invariant approach is sensible (there is no reason why the controller performance should depend on whether the reference trajectory is heading west or south), we show through simulations that the ILQG outperforms the conventional LQG controller in case of large noises or large initial uncertainties. We show that those robustness properties may also prove useful for motion planning applications.